Question

An air capacitor is madeby using two flat plates, each with area A, separated by a distanced . Then a metal slab having thickness a (less than d )and the sameshape and size as the plates is inserted between them, parallel tothe plates and not touching either plate.

a) What is the capacitance of this arrangement?

C = C₀ d/(d-a)

b) Express the capacitance as a multiple of the capacitanceC₀ when the metal slab is not present?

c) Discuss what happens to the capacitance in the limits a--> 0 and a -->d.

Please provided a detailed solution to b and c, which I don'tunderstand how to do. (Wouldn't a be the same as b?)

Thanks,

Answer 1

The capacitance of the parallel plate capacitor is expressed as Capacitance of given arrangement with the metal slab between two flat plates is expressed as, Here, 4 is the area, d is the total thickness along with the flat plates and metal slab, and a is the thickness of the metal slab Capacitance without metal slab is expressed from the above equation as, When the limit a -> 0 is applied, d-0 When the limit a -> dis applied, d-d 0